PRODUCTS
Products Overview
Mathematica
Mathematica Student Edition
Mathematica Home Edition
Wolfram
CDF Player
(free download)
Computable Document Format (CDF)
web
Mathematica
grid
Mathematica
Wolfram
Workbench
Wolfram
SystemModeler
Wolfram
Finance Platform
Mathematica
Add-Ons
Wolfram|Alpha Products
SOLUTIONS
Solutions Overview
Engineering
Aerospace Engineering & Defense
Chemical Engineering
Control Systems
Electrical Engineering
Image Processing
Industrial Engineering
Materials Science
Mechanical Engineering
Operations Research
Optics
Petroleum Engineering
Biotechnology & Medicine
Bioinformatics
Medical Imaging
Finance, Statistics & Business Analysis
Actuarial Sciences
Data Analysis & Mining
Econometrics
Economics
Financial Engineering & Mathematics
Financial Risk Management
Statistics
Software Engineering & Content Delivery
Authoring & Publishing
Interface Development
Software Engineering
Web Development
Science
Astronomy
Biological Sciences
Chemistry
Environmental Sciences
Geosciences
Social & Behavioral Sciences
Design, Arts & Entertainment
Game Design, Special Effects & Generative Art
Education
STEM Education Initiative
Higher Education
Community & Technical College Education
Primary & Secondary Education
Students
Technology
Computable Document Format (CDF)
High-Performance & Parallel Computing (HPC)
See Also: Technology Guide
PURCHASE
Online Store
Other Ways to Buy
Volume & Site Licensing
Contact Sales
Software
Service
Upgrades
Training
Books
Merchandise
SUPPORT
Support Overview
Mathematica
Documentation
Knowledge Base
Learning Center
Technical Services
Community & Forums
Training
Does My Site Have a License?
Wolfram User Portal
COMPANY
About Wolfram Research
News
Events
Wolfram Blog
Partnerships
Employment Opportunities
History of
Mathematica
Stephen Wolfram's Home Page
Contact Us
OUR SITES
All Sites
Wolfram|Alpha
Demonstrations Project
MathWorld
Integrator
Wolfram Functions Site
Mathematica Journal
Wolfram Media
Wolfram
Tones
Wolfram Science
Stephen Wolfram
SEARCH MATHEMATICA 8 DOCUMENTATION
THIS IS DOCUMENTATION FOR AN OBSOLETE PRODUCT.
SEE THE
DOCUMENTATION CENTER
FOR THE LATEST INFORMATION.
Mathematica
>
Bessel-Related Functions
>
Built-in
Mathematica
Symbol
Special Functions
Tutorials »
|
BesselI
AiryAi
BesselJ
KelvinKer
KelvinKei
See Also »
|
Bessel-Related Functions
Functions Used in Quantum Mechanics
Mathematical Functions
Special Functions
More About »
BesselK
BesselK
[
n
,
z
]
gives the modified Bessel function of the second kind
.
MORE INFORMATION
Mathematical function, suitable for both symbolic and numerical manipulation.
satisfies the differential equation
.
BesselK
[
n
,
z
]
has a branch cut discontinuity in the complex
z
plane running from
to
.
FullSimplify
and
FunctionExpand
include transformation rules for
BesselK
.
For certain special arguments,
BesselK
automatically evaluates to exact values.
BesselK
can be evaluated to arbitrary numerical precision.
BesselK
automatically threads over lists.
EXAMPLES
CLOSE ALL
Basic Examples
(3)
Evaluate numerically:
In[1]:=
Out[1]=
Plot
:
In[1]:=
Out[1]=
In[1]:=
Out[1]=
Scope
(6)
Generalizations & Extensions
(1)
Applications
(1)
Properties & Relations
(2)
Possible Issues
(1)
SEE ALSO
BesselI
AiryAi
BesselJ
KelvinKer
KelvinKei
TUTORIALS
Special Functions
RELATED LINKS
MathWorld
The Wolfram Functions Site
MORE ABOUT
Bessel-Related Functions
Functions Used in Quantum Mechanics
Mathematical Functions
Special Functions
New in 1
© 2013 Wolfram Research, Inc.
. 
satisfies the differential equation 
. 
to 
.
EXAMPLES
Basic Examples 
Scope 